Question

In a box there a total of four prizes: Two of them are worth $4, a single prize worth $26, and a single prize worth $241. A player will reach into the box and draw one of the prizes at random. What is the fair price for this game?

Answer 1

So,

First of all, the player has a 1/4 chance of drawing any of the 4 prizes.

This means that the probability of drawing a prize of $4 is 1/2 because there are 2 prizes worth of $4. The probability of drawing a prize of $26 is 1/4 and the probability of drawing a prize of $241 is also 1/4.

To find the fair price, we need to find the expected value of this problem:

This can be obtained by multiplying any possible value of a price for the probability of drawing a prize of that value and adding all these Hvalues together.

This is:

`\begin{gathered} 4\cdot(1)/(2)+26\cdot(1)/(4)+241\cdot(1)/(4) \\ \\ =(275)/(4)=68.75 \end{gathered}`

Therefore, the fair price of this game is $68.75.